Results 11 to 20 of about 228,002 (82)
On Quasi S‐Propermutable Subgroups of Finite Groups
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 A subgroup H of a finite group G is said to be quasi S‐propermutable in G if K⊲¯G such that HK is S‐permutable in G and H ∩ K ≤ HqsG, where HqsG is the subgroup formed by all those subgroups of H which are S‐propermutable in G. In this paper, we give some generalizations of finite group G by using the properties and effects of quasi S‐propermutable ...
Hong Yang +6 more
wiley +1 more source
A Note on the Normal Index and the c‐Section of Maximal Subgroups of a Finite Group
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K ≤ M and G = MH, we called the order of H/K the normal index of M and (M∩H)/K a section of M in G. Using the concepts of normal index and c‐section, we obtain some new characterizations of p‐solvable, 2‐supersolvable, and p‐nilpotent.
Na Tang, Xianhua Li, Junjie Wei
wiley +1 more source
Finite Groups with Some SE‐Supplemented Subgroups
Algebra, Volume 2013, Issue 1, 2013., 2013 Let H be a subgroup of a finite group G, p a prime dividing the order of G, and P a Sylow p‐subgroup of G for prime p. We say that H is SE‐supplemented in G if there is a subgroup K of G such that G = HK and H∩K ≤ HseG, where HseG denotes the subgroup of H generated by all those subgroups of H which are S‐quasinormally embedded in G.
Guo Zhong +5 more
wiley +1 more source
Finite Groups Whose Certain Subgroups of Prime Power Order Are S‐Semipermutable
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Let G be a finite group. A subgroup H of G is said to be S‐semipermutable in G if H permutes with every Sylow p‐subgroup of G with (p, |H|) = 1. In this paper, we study the influence of S‐permutability property of certain abelian subgroups of prime power order of a finite group on its structure.
Mustafa Obaid, A. Kiliçman
wiley +1 more source
Mutually Permutable Products of Finite Groups
International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011 Let G be a finite group and G1, G2 are two subgroups of G. We say that G1 and G2 are mutually permutable if G1 is permutable with every subgroup of G2 and G2 is permutable with every subgroup of G1. We prove that if G = G1G2 = G1G3 = G2G3 is the product of three supersolvable subgroups G1, G2, and G3, where Gi and Gj are mutually permutable for all i ...
Rola A. Hijazi +4 more
wiley +1 more source
A note on p‐solvable and solvable finite groups
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 821-824, 1994., 1994 The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p‐solvable and solvable where p is the largest prime divisor of |G|. These are used further in identifying the largest normal p‐solvable and normal solvable subgroups, respectively, of G.
R. Khazal, N. P. Mukherjee
wiley +1 more source
Maximal subgroups of finite groups
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 2, Page 311-314, 1990., 1989 In finite groups maximal subgroups play a very important role. Results in the literature show that if the maximal subgroup has a very small index in the whole group then it influences the structure of the group itself. In this paper we study the case when the index of the maximal subgroups of the groups have a special type of relation with the Fitting ...
S. Srinivasan
wiley +1 more source
A note on non-solvable groups with given number of particular subgroups
Proceedings of the Romanian Academy. Series A Mathematics, Physics, Technical Sciences, Information ScienceConsidering the quantitative properties of some particular subgroups of a finite group, we prove that (1) a non-solvable group $G$ has exactly 5 non-subnormal non-supersolvable proper subgroups if and only if $G\cong A_5$ or $SL_2(5)$. (2) a non-solvable
Jiangtao Shi, Fanjie Xu, Yifan Liu
semanticscholar +1 more source
A note on finite group structure influenced by second and third maximal subgroups
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 4, Page 747-750, 1990., 1990 The structure of a finite group having specified number of second and third maximal subgroups has been investigated in the paper.
N. P. Mukherjee, R. Khazal
wiley +1 more source
A generalized Frattini subgroup of a finite group
International Journal of Mathematics and Mathematical Sciences, Volume 12, Issue 2, Page 263-266, 1989., 1989 For a finite group G and an arbitrary prime p, let SP(G) denote the intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set SP(G) = G. Some properties of G are considered involving SP(G).
Prabir Bhattacharya, N. P. Mukherjee
wiley +1 more source